A square with side length 49 is completely tiled with the following non-overlapping shapes: 600 1×4 rectangles and a unit square. Find the number of possible locations of the unit square.
(In reply to
re: Parity by Jer)
Well I can show any of my A's does have a tiling. Cut the square into pieces, by splitting along the row and column of the A that we presume to be the untiled square.
A*** A ***A
**** * ****
**** * ****
**** * ****
A*** A ***A
**** * ****
**** * ****
**** * ****
A*** A ***A
There are now nice pieces, the four larger corner pieces will be some multiple of 4 in both directions. The four thin pieces will be 1 by some multiple of 4. All eight of those pieces can be trivially tiled by 1x4 rectangles, leaving just our selected A as the lone untiled square.
I'll have to think about the B's
re(2): Parity
